In the most dramatic changes since the Big East’s inception 21 years ago, the conference announced yesterday that, beginning next season, with the addition of Virginia Tech, its schools will be split into two separate seven-team divisions with the last-place team in each division not coming to The Garden for the Big East Conference Tournament.

The teams in the respective divisions, which have yet to be named, will play each other twice a year. The additional four league games will be feature crossover games between teams in the other division.

“With the divisions, we’re going to have to come up with these [new] rivalries and that’s probably going to take some time,” said Georgetown coach Craig Esherick, who was an assistant coach in the mid-’80s when the Hoyas and St. John’s ruled the league. “You’ll end up not playing some teams one year and I don’t think that that’s a good thing. I wish that everybody was able to play everybody. I think that does take away something from the league. When you’re making decisions like this, football definitely came into play. And that’s something us basketball coaches are just going to have to live with.”

St. John’s will play in what is unofficially being referred to as the New England Division. The Red Storm will play Boston College, Connecticut, Miami, Providence, Villanova and Virginia Tech twice each season.

Traditional Red Storm rivals such as Georgetown and Syracuse are in the other division along with cross-river rivals Seton Hall and Rutgers. In a given season, St. John’s may not play the Hoyas, Orangemen, Pirates and/or Scarlet Knights.

Big East Conference commissioner Mike Tranghese will have sole authority to decide on a yearly basis which teams cross-over and in what format. For example, St. John’s and Syracuse could play a home-and-home series in a given season with the Red Storm then playing two other opponents. Or St. John’s could face four separate opponents from the other division.

The only guarantee is that each school’s four crossover games will consist of two home games and two road games. But the days of St. John’s and Syracuse playing a home-and-home series every year are over.

“Clearly I don’t want one team not seeing another team for a long period of time,” said Tranghese. “That just flies in the face of being in a conference.”

Which is exactly how some coaches and athletic directors feel about all 14 teams not coming to the Garden in March for the Big East Conference Tournament, long considered the crown jewel of the league.

Although the athletic directors voted 13-0 [Virginia Tech, which was admitted to the league in late August, did not have a vote] to approve the new format, Tranghese acknowledged that there are several athletic directors who are, “violently opposed” to not having all the teams come to New York for the conference tournament in March. Virtually every coach expressed a similar concern.

“New York City and the Garden are a great place for the tournament and it’s one of the features we sell our players on,” said Providence coach Tim Welsh. “In an off year, if you don’t make it [to the tournament], it’s obviously going to hurt you in recruiting. You just have to work hard to keep your head above water.”

Tranghese doesn’t dispute that the conference tournament in the World’s Most Famous Arena is one of the league’s marquee attractions. It figures heavily in each school’s recruiting and in the league’s television negotiations.

But these are the problems with a hybrid league which has six members that do not have Division I-A football teams. When the league agreed to add Miami, Rutgers, West Virginia and Virginia Tech to save the football conference, it created a 14-headed basketball monster.

If the 2,000-2,001 season were to end today, based on the new format, Pittsburgh and, in the “New England Division,” either Providence or Boston College would not be coming to the Garden. Some athletic directors were even willing to have their teams play as early as 9 a.m. on the first day of the tournament to avoid being left out.

“We’ve got 14 teams,” Tranghese said. “If you can’t play your way into the top 12 spots, it’s not asking people to accomplish something that is insurmountable. I realize that teams are going to be left out. A couple of coaches said to me, ‘Well if we get left out, then it hurts us.’ If you finish 3-13 in this league, and you’re finishing 13th or 14th place, you’ve got bigger problems than not going to New York City,” Tranghese added.